## 15. ÖMG-Kongress

Jahrestagung der Deutschen Mathematikervereinigung

#### 16. bis 22. September 2001 in Wien

**Sektion 11 - Numerische Mathematik, Wissenschaftliches Rechnen**

Donnerstag, 20. September 2001, 15.30, Hörsaal 47

**Simulation of the Dynamics of Tethered Satellite Systems**
**Hans Troger**, **TU Wien**
(Koautoren: M.Matzl, W.Poth, A.Steindl, G.Wiedermann)

The dynamics of tethered satellite systems, that is an arrangement
of two or more satellites, which are connected by thin long cables in
orbit around a planet, is described by a coupled set of nonlinear
ordinary and partial differential equations. We present the equations
in weak form, which for the system of varying mass composition is
nontrivial. Since the equations are stiff their numerical treatment
requires special measures. One possibility is to introduce an alternative
set of variables (natural string variables) for the description of the
deformation of the tether. In these new variables the equations, to
some extend, decouple with respect to the slow and fast motions.
The discretization of the tether in space is performed by Finite Elements
and by Finite Differences. Two different formulations of the equations
of motion and various time integrators, especially qualified for stiff
systems, are compared with each other. With the developed computer code
some selected (partly animated) simulation results concerning practically
important motions of the tethered satellite system, both with constant
and variable tether length, and applying control will be presented.

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